Finally, we apply our findings to a stochastic feedforward neural networks with ReLU activation. We generalize the setup in [1]} – that builds a bridge between tropical geometry and deep neural networks – by allowing the parameters of the neural network to be stochastic. In particular, in every layer of the neural network we let the weight matrix and the bias vector be stochastic and possibly correlated with the ones in the previous layers. In Proposition REF  we show that the assumption of Theorem REF  is easily satisfied in this setup. In Proposition REF  we prove that the upper bounds for the number of positive and negative regions of the stochastic version of the neural network found in [1]} concentrate around their expected value. Although the tropical geometry of deep neural networks has been further investigated [3]}, [4]}, this is the first time probabilistic results are presented within the framework introduced in [1]}.
